Question

the length of the freeway is 600 miles. if 0.5 inch represents 50 miles, what is the length of the freeway on the map?
a. 10 inches \tc. 12 inches
b. 6 inches \td. 3 inches

please select the best answer from the choices provided

○ a
○ b
○ c
○ d

Explanation:

Step1: Find miles per inch

First, find how many miles 1 inch represents. Since 0.5 inch is 50 miles, 1 inch is \( \frac{50}{0.5} = 100 \) miles per inch.

Step2: Calculate map length

The freeway is 600 miles. So the length on the map is \( \frac{600}{100} = 6 \) inches? Wait, no, wait. Wait, 0.5 inch is 50 miles, so the scale is 0.5 in : 50 mi. So we can set up a proportion. Let \( x \) be the map length. Then \( \frac{0.5}{50} = \frac{x}{600} \). Cross - multiply: \( 50x = 0.5\times600 \). \( 50x = 300 \). Then \( x=\frac{300}{50}=6 \)? Wait, no, wait 0.5 inch is 50 miles, so 1 inch is 100 miles. 600 miles would be 600/100 = 6 inches? But wait, let's check again. Wait, 0.5 inch represents 50 miles, so the number of 50 - mile segments in 600 miles is \( 600\div50 = 12 \). Each segment is 0.5 inch, so total length is \( 12\times0.5 = 6 \) inches? Wait, no, 600 divided by 50 is 12, times 0.5 is 6. Wait, but let's do the proportion correctly. Let \( x \) be the map length in inches. Then \( \frac{x}{600}=\frac{0.5}{50} \). Cross multiply: \( 50x=600\times0.5 \). \( 50x = 300 \). \( x = 300\div50=6 \). Wait, but the options have 6 as option B? Wait, but let's check again. Wait, 0.5 inch is 50 miles, so 1 inch is 100 miles. 600 miles: 600/100 = 6 inches. So the answer is B. 6 inches.

Answer:

B. 6 inches